%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:42:29 PM UTC 2026
% Result : Theorem 5.48s 2.09s
% Output : Refutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 10 unt; 2 def)
% Number of atoms : 134 ( 27 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 161 ( 61 ~; 57 |; 30 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 40 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> in(apply(X1,X0),relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> in(apply(X1,X0),relation_rng(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f57,plain,
? [X0,X1] :
( ~ in(apply(X1,X0),relation_rng(X1))
& in(X0,relation_dom(X1))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f58,plain,
? [X0,X1] :
( ~ in(apply(X1,X0),relation_rng(X1))
& in(X0,relation_dom(X1))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f59]) ).
fof(f70,plain,
( ~ in(apply(sK10,sK9),relation_rng(sK10))
& in(sK9,relation_dom(sK10))
& relation(sK10)
& function(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f58]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f60]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK11(X0,X1) )
| ~ in(sK11(X0,X1),X1) )
& ( ( in(sK12(X0,X1),relation_dom(X0))
& sK11(X0,X1) = apply(X0,sK12(X0,X1)) )
| in(sK11(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK13(X0,X5),relation_dom(X0))
& apply(X0,sK13(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X2,sK11(X0,X1)),skolemize(X4,sK12(X0,X1)),skolemize(X7,sK13(X0,X5))],[f72]) ).
fof(f112,plain,
function(sK10),
inference(cnf_transformation,[],[f70]) ).
fof(f113,plain,
relation(sK10),
inference(cnf_transformation,[],[f70]) ).
fof(f114,plain,
in(sK9,relation_dom(sK10)),
inference(cnf_transformation,[],[f70]) ).
fof(f115,plain,
~ in(apply(sK10,sK9),relation_rng(sK10)),
inference(cnf_transformation,[],[f70]) ).
fof(f118,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f122,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f118]) ).
fof(f123,plain,
! [X0,X6] :
( ~ function(X0)
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f122]) ).
fof(f220,plain,
! [X0] :
( ~ in(X0,relation_dom(sK10))
| ~ relation(sK10)
| in(apply(sK10,X0),relation_rng(sK10)) ),
inference(resolution,[],[f123,f112]) ).
fof(f231,definition,
( spl15_14
<=> relation(sK10) ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
fof(f232,plain,
( ~ relation(sK10)
| spl15_14 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f234,definition,
( spl15_15
<=> ! [X0] :
( ~ in(X0,relation_dom(sK10))
| in(apply(sK10,X0),relation_rng(sK10)) ) ),
introduced(definition,[new_symbols(definition,[spl15_15])],[avatar_definition]) ).
fof(f235,plain,
( ! [X0] :
( in(apply(sK10,X0),relation_rng(sK10))
| ~ in(X0,relation_dom(sK10)) )
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f236,plain,
( ~ spl15_14
| spl15_15 ),
inference(avatar_split_clause,[],[f220,f234,f231]) ).
fof(f237,plain,
( $false
| spl15_14 ),
inference(resolution,[],[f232,f113]) ).
fof(f239,plain,
spl15_14,
inference(avatar_contradiction_clause,[],[f237]) ).
fof(f240,plain,
( ~ in(sK9,relation_dom(sK10))
| ~ spl15_15 ),
inference(resolution,[],[f235,f115]) ).
fof(f247,plain,
( $false
| ~ spl15_15 ),
inference(resolution,[],[f240,f114]) ).
fof(f248,plain,
~ spl15_15,
inference(avatar_contradiction_clause,[],[f247]) ).
cnf(s9,plain,
( ~ spl15_14
| spl15_15 ),
inference(sat_conversion,[],[f236]) ).
cnf(s10,plain,
spl15_14,
inference(sat_conversion,[],[f239]) ).
cnf(s12,plain,
~ spl15_15,
inference(sat_conversion,[],[f248]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s9,s12,s10]) ).
fof(f249,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:24:31 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.48/2.09 % (2227731)Detected formulas, will run a generic FOF schedule.
% 5.48/2.09 % (2227755)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3914361294:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.48/2.09 % (2227761)dis-21_1_sil=8000:lcm=predicate:random_seed=2755576093:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.48/2.09 % (2227761)First to succeed.
% 5.48/2.09 % (2227761)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2227731"
% 5.48/2.09 % (2227760)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1648251477:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.48/2.09 % (2227760)Also succeeded, but the first one will report.
% 5.48/2.09 % (2227758)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=143372706:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.48/2.09 % (2227756)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1775193930:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.48/2.09 % (2227759)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3652758906:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.48/2.09 % (2227757)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=120280604:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.48/2.09 % (2227758)Also succeeded, but the first one will report.
% 5.48/2.09 % (2227759)Also succeeded, but the first one will report.
% 5.48/2.09 % (2227761)Refutation found. Thanks to Tanya!
% 5.48/2.09 % SZS status Theorem for theBenchmark
% 5.48/2.09 % SZS output start Proof for theBenchmark
% See solution above
% 5.48/2.09 % (2227761)------------------------------
% 5.48/2.09 % (2227761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.09 % (2227761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.09 % (2227761)CaDiCaL version: 2.1.3
% 5.48/2.09 % (2227761)Termination reason: Refutation
% 5.48/2.09 % (2227761)Time elapsed: 0.007 s
% 5.48/2.09 % (2227761)Peak memory usage: 89 MB
% 5.48/2.09 % (2227761)Instructions burned: 4 (million)
% 5.48/2.09 % (2227761)------------------------------
% 5.48/2.09 % (2227761)------------------------------
% 5.48/2.09 % (2227731)Success in time 0.629 s
% 5.48/2.09 % Vampire exiting
%------------------------------------------------------------------------------